Cuneiform writing was invented by the ancient Sumerians around 3500 B.C. Hieroglyphic writing was invented by the ancient Egyptians around 3200 B.C.
The two forms of writing differed from each other in at least the following ways:
Hieroglyphic writing represented consonants only. Cuneiform script represented whole syllables, including the vowels.
Although cuneiform script began as picture writing, its symbols rapidly evolved into abstract shapes that, in most cases, bore no resemblance to any actual object. Egyptian hieroglyphs remained recognizable pictures throughout the 3500-year history of the script.
Over its long history, cuneiform writing was adapted to the needs of a large number of languages, including the original Sumerian, Akkadian, Hittite, Elamite, Eblaite and Old Persian. Egyptian hieroglyphs were never applied to any language other than Egyptian itself.
The hieroglyphic writing system was ONLY used for ancient EGYPTIAN. The cuneiform writing system, started by the Sumerians, was then picked up and widely used by the Mesopotamian speakers of a Semitic** language unrelated to Sumerian -- the language of the Babylonians and retricerians, called "Akkadian" by modern scholars. From there it spread further and was used to write other languages - esp. Elamite and Hittite.